Post by Steve Yenisch on May 14, 2009 11:41:41 GMT -5
Paper: www.mae.ufl.edu/nkim/ISSMO/ShikuiChenPaper.pdf
Presentation: www.mae.ufl.edu/nkim/ISSMO/ShikuiChenPresentation.pdf
ABSTRACT
In this paper, we attempt to address the cutting-edge problem of robust shape and topology optimization (RSTO) of compliant mechanisms with consideration of random field uncertainty, such as material property. The proposed approach is based on the state-of-the art level set methods for shape and topology optimization and the latest research development in design under uncertainty. Conventional robust design, usually posed as a continuous optimization problem in finite dimensions, is extended to an infinite-dimensional shape and topology optimization problem and uncertainty is considered as a new dimension in addition to space and time. We illustrate that a level-set-based RSTO problem can be mathematically formulated by expressing the statistical moments of a response as functionals of geometric shapes and random field. To characterize the high-dimensional random-field material uncertainty with a reduced set of random variables, the Karhunen-Loeve expansion is employed, which is essentially a spectral representation of the random field using a reduced set of random variables and the eigenfunctions of its covariance function as expansion bases. Once the reduced set of random variables is identified, the univariate dimension-reduction (UDR) quadrature rule is employed for calculating statistical moments of the design response. The combination of the above techniques not only greatly reduces the computational cost in evaluating the statistical moments but also enables a semi-analytical approach that introduces the shape sensitivity of the statistical moments using shape sensitivity analysis. The application of our approach to compliant mechanism design shows that the proposed RSTO method can lead to designs with completely different topologies and superior robustness compared to their deterministic counterparts. Although the current contents of this paper are focused on Gauss-type material uncertainties, the proposed method is generic and can be easily extended to robust topology optimization subject to other types of uncertainties, such as Gauss/Non-Gauss type loading and geometric uncertainties.
Presentation: www.mae.ufl.edu/nkim/ISSMO/ShikuiChenPresentation.pdf
Robust Shape and Topology Optimization of Compliant Mechanisms Considering Random Field Uncertainty
Shikui Chen, Wei Chen and Sanghoon Lee
Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA, weichen@northwestern.edu
Shikui Chen, Wei Chen and Sanghoon Lee
Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA, weichen@northwestern.edu
ABSTRACT
In this paper, we attempt to address the cutting-edge problem of robust shape and topology optimization (RSTO) of compliant mechanisms with consideration of random field uncertainty, such as material property. The proposed approach is based on the state-of-the art level set methods for shape and topology optimization and the latest research development in design under uncertainty. Conventional robust design, usually posed as a continuous optimization problem in finite dimensions, is extended to an infinite-dimensional shape and topology optimization problem and uncertainty is considered as a new dimension in addition to space and time. We illustrate that a level-set-based RSTO problem can be mathematically formulated by expressing the statistical moments of a response as functionals of geometric shapes and random field. To characterize the high-dimensional random-field material uncertainty with a reduced set of random variables, the Karhunen-Loeve expansion is employed, which is essentially a spectral representation of the random field using a reduced set of random variables and the eigenfunctions of its covariance function as expansion bases. Once the reduced set of random variables is identified, the univariate dimension-reduction (UDR) quadrature rule is employed for calculating statistical moments of the design response. The combination of the above techniques not only greatly reduces the computational cost in evaluating the statistical moments but also enables a semi-analytical approach that introduces the shape sensitivity of the statistical moments using shape sensitivity analysis. The application of our approach to compliant mechanism design shows that the proposed RSTO method can lead to designs with completely different topologies and superior robustness compared to their deterministic counterparts. Although the current contents of this paper are focused on Gauss-type material uncertainties, the proposed method is generic and can be easily extended to robust topology optimization subject to other types of uncertainties, such as Gauss/Non-Gauss type loading and geometric uncertainties.